when cold booting my notebook (Packard Bell EasyNote MV51) the screen is completely black. This is NOT a hardware defect, although:

- No BIOS boot screen of notebook (the BIOS boot image) which shows "Packard Bell" screen. This is not the BIOS SETTINGS menu, but the very first graphical image normally displayed on screen everytime notebook boots,

- no X-server graphical screen, although binary NVIDIA module is being loaded in background.

I reboot several times without anything changing, then suddenly:
- I get BIOS screen image,
- I can see boot messages,
- I can see NVIDIA message indicating binary NVIDIA being loaded.

Sometimes any of these steps gets skipped, i.e. I still don't get the BIOS screen image but then I see boot messages, or I don't get the BIOS screen image and I don't get the boot messages but the NVIDIA message that driver is loading.

BUT:

I do not know why firstly nothing is displayed, and then it all works normal.

What can I do?

I have done all d-u, driver is latest NVIDIA binary driver (normal driver and later updated to beta driver, symptoms are the same. Have used nouveau driver also, same symptoms).

If you don't see the BIOS screens (the one using "Packard Bell") and grub, then the problem is not software side but faulty hardware. It may possibly be a BIOS issue at most, but more likely is a broken hardware component that only starts working once it reaches a certain temperature.

As slh already stated, your symptoms happen way before any OS or software-bootmanager start to work. So you might find more related help when searching for similar problems in some hardware-forum.
Some notebooks might behave strange when there is some mismatch with energysettings in Bios, look for LCD/Graphics/Energy/Boottime related settings there.
You can try if something changes when you boot completely without batterypack, powercord only. Or try pressing and holding the powerbutton for ~30 seconds. Or connect to an external monitor to see if only your display has some loose contact while the external monitor shows a picture. If you are experienced enough (at your own risk, obviously), unscrew and open the respective covers to see if all devices, cables and RAM sit straight in their places. But from my experience with other notebooks, from your symptoms I'm afraid your onboard-graphics needs service .